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Mensuration - Quant/Math - CAT 2008
Question 4 the day:
July 31, 2003
The question for the day is from the topic of Mensuration.
- A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?
| (1) |
1 : 6 |
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(2) |
1 : 5 |
| (3) |
1 : 25 |
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(4) |
1 : 125 |
Correct Answer - (2)
Solution:
The volume of the larger cube = 53 = 125 cm3.
The volume of each of the smaller cubes = 13 = 1 cm3. Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a2 = 6(52) = 6 * 25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm3 cubes = 125 * 6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5
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